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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.3 Summation versus Integration, #21 · Calculus · Integrals

Suppose … has the form

Suppose $f_{n}$ has the form $an + b n^{2} + c n^{3}$ . If you know
$f_{1} = 1, f_{2} = 5, f_{3} = 14$ , turn those into three equations for
$a, b, c$ . The solutions $a = \frac{1}{6}, b = \frac{1}{2}, c = \frac{1}{3}$ give what formula?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.3 Summation versus Integration, #21

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